[FOM] The unreasonable soundness of mathematics

[Timothy Y. Chow]

On Sun, 15 May 2016, Daniel Mehkeri wrote:
> Ultrafinitism is about feasibility, addition and multiplication are 
> feasible operations, while exponentiation isn't.

O.K., this is one definition of ultrafinitism.  It isn't the definition of 
ultrafinitism I had in mind, and I agree with you that my original 
argument about "unreasonable soundness" doesn't directly apply to 
ultrafinitism as you have defined it.  Maybe, from your perspective, the 
version of ultrafinitism I have in mind is a strawman; I'm O.K. with that.

Although I did say that I did not want to debate "what Nelson believed," I 
will point out the following MathOverflow question:

http://mathoverflow.net/questions/142669/illustrating-edward-nelsons-worldview-with-nonstandard-models-of-arithmetic

Nelson himself answered the question and engaged in some back-and-forth in 
the comments.  Based on Nelson's remarks, I believe that Nelson did not 
simply hold that "multiplication is feasible and exponentiation is not" or 
some such.  But let us not argue that point on FOM; I just wanted to let 
you know of the existence of these comments by Nelson.

Tim